The entropy-like measures, each quantifying a single spreading facet, are of local (Fisher information) or global (Rényi and Shannon entropies) character depending whether they are very sensitive to the fluctuations of the density or not, respectively. The Fisher information \(F(\rho )\) , which is the most familiar and relevant local entropic measure [1]}, [2]}, is a functional of the derivative of the density \(\rho (x)\) . Then, it controls the localization of the density around its nodes, appropriately grasping the oscillatory nature of the density. This allows it to characterize a great diversity of scientific phenomena which are closely connected to the kinetic and Weizsäcker energies [3]}, [4]}, [5]} of the quantum systems. The Rényi entropies \(R_{q}[\rho ],\, q \ne 1,\,\)[6]}, [7]}, which depend on a real parameter \(q\) , and its limiting case \(q\rightarrow 1\) , the Shannon entropy \(S[\rho ]\)  [8]}, [9]}, are the most important global spreading measures. They are \(q\) -power functionals of the density, closely related to the algebraic \(\mathfrak {L}_{q}\) -norms of the involved HOPs. Then, they can describe many quantities of great scientific and technological interest, such as e.g. the thermodynamical entropy in the case of a thermal ensemble and the disequilibrium when \(q \rightarrow 1\)  and 2, respectively; moreover, they are the basic variables of the classical and quantum information theories [9]}, [11]}, [12]}.
